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Ray-normal mode and hybrid analysis of transient waves in a finite beam. (English) Zbl 0920.73185
Summary: General solutions for wave propagation in a beam with semi-infinite or finite length based on the Timoshenko theory are presented. The solutions are derived on the basis of the ray theory, the normal mode theory, and a hybrid formulation which combines these two theories to generate a solution valid for short time and near field as well as long time and far field. All three formulations can be formulated rigorously from a unified treatment of the inverse integral transforms. Finite beams with fixed, hinged, or free boundary conditions are considered, and a numerical example is shown to illustrate the comparison of three methods.
MSC:
74H45Vibrations (dynamical problems in solid mechanics)
74K10Rods (beams, columns, shafts, arches, rings, etc.) in solid mechanics